Maxwell Boltzmann Speed Distribution

AI Thread Summary
In the discussion about the Maxwell Boltzmann speed distribution, it is clarified that Vmost probable, Vaverage, and Vrms differ in three dimensions. When restricted to one dimension, these quantities do not equal each other. Vmost probable is identified as the peak of the distribution curve, while Vaverage is also suggested to align with this peak at V=0. The definition and calculation of Vrms, or root mean square velocity, are questioned, indicating a need for a mathematical formula for clarity. Understanding these distinctions is crucial for analyzing gas behavior in different dimensional contexts.
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Homework Statement



The three quantities Vmost probable, Vaverage, and Vrms, are not the same for the Maxwell speed distribution in 3D. If you restrict the gas to only be one dimensional, are these three quantities equal to each other? Justify your answer with a short explanation.

Homework Equations


The Attempt at a Solution


The curve looks like gaussian curve. I know Vmostprobable is going to be the peak of the curve. And Vaverage would also be at the peak of the curve which is at V=0. I am not sure how to get Vrms
 
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What's the definition of ##v_\text{rms}##?
 
Root mean square velocity
 
I was looking for perhaps a mathematical formula or some other indication that you know what those words mean.
 
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